Question

What is the least common denominator of `5/x^2 - 3/(6x^2 + 12x)`?

Answer 1

See a solution process below:

Explanation:

First, find the factors for each of the denominators individually:

`x^2 = x * x`

`6x^2 + 12x = 6 * x * (x + 2)`

The common factor is: `x`

Removing this leaves the following factors from each of the terms:

`x` and `6 * (x + 2)`

We need to multiply the fraction on the left by `6(x + 2)` to obtain a common denominator:

`(6(x + 2))/(6(x + 2)) xx 5/x^2 => (5 * 6(x + 2))/(x^2 * 6(x + 2)) => (30(x + 2))/(6x^2(x + 2))`

We need to multiply the fraction on the right by `x/x` to obtain a common denominator:

`x/x xx 3/(6x^2 + 12x) => (3 * x)/(x(6x^2 + 12x)) => (3x)/(6x^3 + 12x^2) =>`

`(3x)/(6x^2(x + 2))`